In Visual Basics

6.Two String returning functions to have nice looking output for numbers/money are?

7.Where do we place a class-level variable declaration, and where is it accessible from?

8.Two forms of parameter passing:

9.FULLY define an array:

10.Show the VB code to declare an initialize an array called Ar1 of Integers to hold the value of 5, 10 and 15.

11. For Ar1above, Ar1.Count = ________ and legal index values are:_____ to ______.

12.Show the VB code to declare an initialize an array Ar2 of Integers to hold 50 zeros.

13. Now write a for loop to set Ar2 to hold the values 0, 1, 2, etc, to 49 [Do NOT hardwire a “49” into thisfor-loop but rather use an expression for the upper bound]. (Hint: 3 lines)

14.Show the VB code to declare an array Ar3 of Strings with size and content to be determined later.

15.Show the VB line needed to fill Ar3 (from above) with the contents of a text file called

“C:\VB2010\MyData.txt”.

Design a 4x4 Sequential Multiplier Circuit

Design a sequential circuit to calculate the product of two 4-bit binary numbers, and then display the decimal result in three HEX displays. Design the circuit at the register transfer level. The inputs include two 4-bit binary numbers, one clock signal, one reset, and one start. The output includes one 8-bit binary number, one ready signal. The sequential circuit uses adder only, and does not use combinational multiplier. Using basic gates : Counter, Register, Shift register, Adder. The design shall have two circuits: A main circuit, A controller circuit.

5. Costs in the short run versus in the long run

Ike’s Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company’s short-run average total cost (SRATC) each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.)

Suppose Ike’s Bikes is currently producing 100 bikes per month in its only factory. Its short-run average total cost is

per bike.

Suppose Ike’s Bikes is expecting to produce 100 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using   .

On the following graph, plot the three SRATC curves for Ike’s Bikes from the previous table. Specifically, use the green points (triangle symbol) to plot its SRATC curve if it operates one factory (SRATC1SRATC1); use the purple points (diamond symbol) to plot its SRATC curve if it operates two factories (SRATC2SRATC2); and use the orange points (square symbol) to plot its SRATC curve if it operates three factories (SRATC3SRATC3). Finally, plot the long-run average total cost (LRATC) curve for Ike’s Bikes using the blue points (circle symbol).

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

SRATC1SRATC2SRATC3LRATC05010015020025030035040036032028024020016012080400AVERAGE TOTAL COST (Dollars per bike)QUANTITY (Bikes)

In the following table, indicate whether the long-run average cost curve exhibits economies of scale, constant returns to scale, or diseconomies of scale for each range of bike production.

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 11 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

What are we testing in this problem?

difference of means

single proportion    

single mean

difference of proportions

paired difference

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ = μ₂; H₁: μ₁ > μ₂

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂    

H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

H₀: μ₁ > μ₂; H₁: μ₁ = μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.    

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.500

0.250 < P-value < 0.500   

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.

There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.    

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 19 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 61 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

What are we testing in this problem?

paired differencedifference of means    single meandifference of proportionssingle proportion

What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ ≤ μ₂; H₁: μ₁ > μ₂H₀: μ₁ ≠ μ₂; H₁: μ₁ = μ₂    H₀: μ₁ ≥ μ₂; H₁: μ₁ < μ₂H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations.    The Student's t. We assume that both population distributions are approximately normal with known population standard deviations.The standard normal. We assume that both population distributions are approximately normal with known population standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


Estimate the P-value.

P-value > 0.5000.250 < P-value < 0.500    0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.   

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 46randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 15 minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of 62 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

a. What are we testing in this problem?

single meansingle proportion     

difference of proportions

difference of means

paired difference

b. What is the level of significance?


c. State the null and alternate hypotheses.

H₀: μ₁ ≤ μ₂; H₁: μ₁ > μ₂

H₀: μ₁ ≠ μ₂; H₁: μ₁ = μ₂     

H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂

H₀: μ₁ ≥ μ₂; H₁: μ₁ < μ₂

d. What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with known population standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown population standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown population standard deviations.

The Student's t. We assume that both population distributions are approximately normal with known population standard deviations.

e. What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


f. Estimate the P-value.

P-value > 0.500

0.250 < P-value < 0.500     

0.100 < P-value < 0.250

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

g. Sketch the sampling distribution and show the area corresponding to the P-value.

h. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

i. Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.

There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.    

A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 15 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

What are we testing in this problem?

difference of proportionssingle proportion    single meandifference of meanspaired difference

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ > μ₂; H₁: μ₁ = μ₂H₀: μ₁ = μ₂; H₁: μ₁ > μ₂    H₀: μ₁ = μ₂; H₁: μ₁ ≠ μ₂H₀: μ₁ = μ₂; H₁: μ₁ < μ₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.    The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.5000.250 < P-value < 0.500    0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.

You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $145 and a 50% chance of decreasing to $71. The risk-free rate of interest is 9%. Calculate the call option's value using the two-state stock price model.

6.There are two assets in one portfolio, X and Y. The weight for Asset X is 48%.

Asset X has a 50-50 chance of earning a return of 10% or 20%.

Asset Y's expected return is 23% and the standard deviation is 33%.

Assume the correlation coefficient between X and Y is 0.53.

Calcualte the expected return of the portfolio.

Calculate the standard deviation of the portfolio return.

You are attempting to value a call option with an exercise price of $108 and one year to expiration. The underlying stock pays no dividends, its current price is $108, and you believe it has a 50% chance of increasing to $133 and a 50% chance of decreasing to $83. The risk-free rate of interest is 9%. Calculate the call option’s value using the two-state stock price model.